LMFDB - Embedded newform 4830.2.a.bg.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$38.5677441763$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} -6.00000 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -4.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} -2.00000 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +1.00000 q^{30} -6.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} -4.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} +6.00000 q^{37} -6.00000 q^{38} -6.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} -1.00000 q^{42} +6.00000 q^{43} -2.00000 q^{44} +1.00000 q^{45} +1.00000 q^{46} +2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -4.00000 q^{51} -6.00000 q^{52} +2.00000 q^{53} +1.00000 q^{54} -2.00000 q^{55} -1.00000 q^{56} -6.00000 q^{57} -12.0000 q^{59} +1.00000 q^{60} -14.0000 q^{61} -6.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} -2.00000 q^{66} -2.00000 q^{67} -4.00000 q^{68} +1.00000 q^{69} -1.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} -14.0000 q^{73} +6.00000 q^{74} +1.00000 q^{75} -6.00000 q^{76} +2.00000 q^{77} -6.00000 q^{78} -16.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -2.00000 q^{83} -1.00000 q^{84} -4.00000 q^{85} +6.00000 q^{86} -2.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} +6.00000 q^{91} +1.00000 q^{92} -6.00000 q^{93} +2.00000 q^{94} -6.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} +1.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	1.00000	0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	−2.00000	−0.426401
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.00000	−1.17670
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	1.00000	0.182574
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	−4.00000	−0.685994
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−6.00000	−0.973329
$39$	−6.00000	−0.960769
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−1.00000	−0.154303
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−2.00000	−0.301511
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−4.00000	−0.560112
$52$	−6.00000	−0.832050
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	1.00000	0.136083
$55$	−2.00000	−0.269680
$56$	−1.00000	−0.133631
$57$	−6.00000	−0.794719
$58$	0	0
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	1.00000	0.129099
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−6.00000	−0.762001
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	−2.00000	−0.246183
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−4.00000	−0.485071
$69$	1.00000	0.120386
$70$	−1.00000	−0.119523
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	1.00000	0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	6.00000	0.697486
$75$	1.00000	0.115470
$76$	−6.00000	−0.688247
$77$	2.00000	0.227921
$78$	−6.00000	−0.679366
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	−1.00000	−0.109109
$85$	−4.00000	−0.433861
$86$	6.00000	0.646997
$87$	0	0
$88$	−2.00000	−0.213201
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	0.105409
$91$	6.00000	0.628971
$92$	1.00000	0.104257
$93$	−6.00000	−0.622171
$94$	2.00000	0.206284
$95$	−6.00000	−0.615587
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	1.00000	0.101015
$99$	−2.00000	−0.201008
$100$	1.00000	0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−4.00000	−0.396059
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−6.00000	−0.588348
$105$	−1.00000	−0.0975900
$106$	2.00000	0.194257
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	1.00000	0.0962250
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	−2.00000	−0.190693
$111$	6.00000	0.569495
$112$	−1.00000	−0.0944911
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−6.00000	−0.561951
$115$	1.00000	0.0932505
$116$	0	0
$117$	−6.00000	−0.554700
$118$	−12.0000	−1.10469
$119$	4.00000	0.366679
$120$	1.00000	0.0912871
$121$	−7.00000	−0.636364
$122$	−14.0000	−1.26750
$123$	−6.00000	−0.541002
$124$	−6.00000	−0.538816
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	6.00000	0.528271
$130$	−6.00000	−0.526235
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−2.00000	−0.174078
$133$	6.00000	0.520266
$134$	−2.00000	−0.172774
$135$	1.00000	0.0860663
$136$	−4.00000	−0.342997
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	1.00000	0.0851257
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	−1.00000	−0.0845154
$141$	2.00000	0.168430
$142$	6.00000	0.503509
$143$	12.0000	1.00349
$144$	1.00000	0.0833333
$145$	0	0
$146$	−14.0000	−1.15865
$147$	1.00000	0.0824786
$148$	6.00000	0.493197
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	1.00000	0.0816497
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−6.00000	−0.486664
$153$	−4.00000	−0.323381
$154$	2.00000	0.161165
$155$	−6.00000	−0.481932
$156$	−6.00000	−0.480384
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−16.0000	−1.27289
$159$	2.00000	0.158610
$160$	1.00000	0.0790569
$161$	−1.00000	−0.0788110
$162$	1.00000	0.0785674
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	−6.00000	−0.468521
$165$	−2.00000	−0.155700
$166$	−2.00000	−0.155230
$167$	−14.0000	−1.08335	−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000	−1.08335	−0.541676	+	0.840587i	$0.682210\pi$
$168$	−1.00000	−0.0771517
$169$	23.0000	1.76923
$170$	−4.00000	−0.306786
$171$	−6.00000	−0.458831
$172$	6.00000	0.457496
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	−2.00000	−0.150756
$177$	−12.0000	−0.901975
$178$	10.0000	0.749532
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	1.00000	0.0745356
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	6.00000	0.444750
$183$	−14.0000	−1.03491
$184$	1.00000	0.0737210
$185$	6.00000	0.441129
$186$	−6.00000	−0.439941
$187$	8.00000	0.585018
$188$	2.00000	0.145865
$189$	−1.00000	−0.0727393
$190$	−6.00000	−0.435286
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	1.00000	0.0721688
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	2.00000	0.143592
$195$	−6.00000	−0.429669
$196$	1.00000	0.0714286
$197$	−14.0000	−0.997459	−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000	−0.997459	−0.498729	+	0.866758i	$0.666200\pi$
$198$	−2.00000	−0.142134
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	1.00000	0.0707107
$201$	−2.00000	−0.141069
$202$	10.0000	0.703598
$203$	0	0
$204$	−4.00000	−0.280056
$205$	−6.00000	−0.419058
$206$	8.00000	0.557386
$207$	1.00000	0.0695048
$208$	−6.00000	−0.416025
$209$	12.0000	0.830057
$210$	−1.00000	−0.0690066
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	2.00000	0.137361
$213$	6.00000	0.411113
$214$	−4.00000	−0.273434
$215$	6.00000	0.409197
$216$	1.00000	0.0680414
$217$	6.00000	0.407307
$218$	18.0000	1.21911
$219$	−14.0000	−0.946032
$220$	−2.00000	−0.134840
$221$	24.0000	1.61441
$222$	6.00000	0.402694
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	6.00000	0.399114
$227$	14.0000	0.929213	0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000	0.929213	0.464606	+	0.885517i	$0.346196\pi$
$228$	−6.00000	−0.397360
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	1.00000	0.0659380
$231$	2.00000	0.131590
$232$	0	0
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	−6.00000	−0.392232
$235$	2.00000	0.130466
$236$	−12.0000	−0.781133
$237$	−16.0000	−1.03931
$238$	4.00000	0.259281
$239$	−18.0000	−1.16432	−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000	−1.16432	−0.582162	+	0.813073i	$0.697793\pi$
$240$	1.00000	0.0645497
$241$	−20.0000	−1.28831	−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000	−1.28831	−0.644157	+	0.764894i	$0.722792\pi$
$242$	−7.00000	−0.449977
$243$	1.00000	0.0641500
$244$	−14.0000	−0.896258
$245$	1.00000	0.0638877
$246$	−6.00000	−0.382546
$247$	36.0000	2.29063
$248$	−6.00000	−0.381000
$249$	−2.00000	−0.126745
$250$	1.00000	0.0632456
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	−1.00000	−0.0629941
$253$	−2.00000	−0.125739
$254$	−2.00000	−0.125491
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	6.00000	0.373544
$259$	−6.00000	−0.372822
$260$	−6.00000	−0.372104
$261$	0	0
$262$	12.0000	0.741362
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−2.00000	−0.123091
$265$	2.00000	0.122859
$266$	6.00000	0.367884
$267$	10.0000	0.611990
$268$	−2.00000	−0.122169
$269$	30.0000	1.82913	0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000	1.82913	0.914566	+	0.404436i	$0.132532\pi$
$270$	1.00000	0.0608581
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	−4.00000	−0.242536
$273$	6.00000	0.363137
$274$	−6.00000	−0.362473
$275$	−2.00000	−0.120605
$276$	1.00000	0.0601929
$277$	−16.0000	−0.961347	−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000	−0.961347	−0.480673	+	0.876900i	$0.659608\pi$
$278$	12.0000	0.719712
$279$	−6.00000	−0.359211
$280$	−1.00000	−0.0597614
$281$	8.00000	0.477240	0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000	0.477240	0.238620	+	0.971113i	$0.423305\pi$
$282$	2.00000	0.119098
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	6.00000	0.356034
$285$	−6.00000	−0.355409
$286$	12.0000	0.709575
$287$	6.00000	0.354169
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	2.00000	0.117242
$292$	−14.0000	−0.819288
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	1.00000	0.0583212
$295$	−12.0000	−0.698667
$296$	6.00000	0.348743
$297$	−2.00000	−0.116052
$298$	−2.00000	−0.115857
$299$	−6.00000	−0.346989
$300$	1.00000	0.0577350
$301$	−6.00000	−0.345834
$302$	0	0
$303$	10.0000	0.574485
$304$	−6.00000	−0.344124
$305$	−14.0000	−0.801638
$306$	−4.00000	−0.228665
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	2.00000	0.113961
$309$	8.00000	0.455104
$310$	−6.00000	−0.340777
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	−6.00000	−0.339683
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−2.00000	−0.112867
$315$	−1.00000	−0.0563436
$316$	−16.0000	−0.900070
$317$	−10.0000	−0.561656	−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000	−0.561656	−0.280828	+	0.959758i	$0.590609\pi$
$318$	2.00000	0.112154
$319$	0	0
$320$	1.00000	0.0559017
$321$	−4.00000	−0.223258
$322$	−1.00000	−0.0557278
$323$	24.0000	1.33540
$324$	1.00000	0.0555556
$325$	−6.00000	−0.332820
$326$	−8.00000	−0.443079
$327$	18.0000	0.995402
$328$	−6.00000	−0.331295
$329$	−2.00000	−0.110264
$330$	−2.00000	−0.110096
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−2.00000	−0.109764
$333$	6.00000	0.328798
$334$	−14.0000	−0.766046
$335$	−2.00000	−0.109272
$336$	−1.00000	−0.0545545
$337$	36.0000	1.96104	0.980522	−	0.196407i	$-0.0629273\pi$
$337$	36.0000	1.96104	0.980522	+	0.196407i	$0.0629273\pi$
$338$	23.0000	1.25104
$339$	6.00000	0.325875
$340$	−4.00000	−0.216930
$341$	12.0000	0.649836
$342$	−6.00000	−0.324443
$343$	−1.00000	−0.0539949
$344$	6.00000	0.323498
$345$	1.00000	0.0538382
$346$	0	0
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	0	0
$349$	−8.00000	−0.428230	−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000	−0.428230	−0.214115	+	0.976808i	$0.568687\pi$
$350$	−1.00000	−0.0534522
$351$	−6.00000	−0.320256
$352$	−2.00000	−0.106600
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	−12.0000	−0.637793
$355$	6.00000	0.318447
$356$	10.0000	0.529999
$357$	4.00000	0.211702
$358$	4.00000	0.211407
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	1.00000	0.0527046
$361$	17.0000	0.894737
$362$	10.0000	0.525588
$363$	−7.00000	−0.367405
$364$	6.00000	0.314485
$365$	−14.0000	−0.732793
$366$	−14.0000	−0.731792
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	1.00000	0.0521286
$369$	−6.00000	−0.312348
$370$	6.00000	0.311925
$371$	−2.00000	−0.103835
$372$	−6.00000	−0.311086
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	8.00000	0.413670
$375$	1.00000	0.0516398
$376$	2.00000	0.103142
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	−6.00000	−0.307794
$381$	−2.00000	−0.102463
$382$	12.0000	0.613973
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.00000	0.0510310
$385$	2.00000	0.101929
$386$	10.0000	0.508987
$387$	6.00000	0.304997
$388$	2.00000	0.101535
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	−6.00000	−0.303822
$391$	−4.00000	−0.202289
$392$	1.00000	0.0505076
$393$	12.0000	0.605320
$394$	−14.0000	−0.705310
$395$	−16.0000	−0.805047
$396$	−2.00000	−0.100504
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	4.00000	0.200502
$399$	6.00000	0.300376
$400$	1.00000	0.0500000
$401$	20.0000	0.998752	0.499376	−	0.866385i	$-0.333563\pi$
$401$	20.0000	0.998752	0.499376	+	0.866385i	$0.333563\pi$
$402$	−2.00000	−0.0997509
$403$	36.0000	1.79329
$404$	10.0000	0.497519
$405$	1.00000	0.0496904
$406$	0	0
$407$	−12.0000	−0.594818
$408$	−4.00000	−0.198030
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	−6.00000	−0.296319
$411$	−6.00000	−0.295958
$412$	8.00000	0.394132
$413$	12.0000	0.590481
$414$	1.00000	0.0491473
$415$	−2.00000	−0.0981761
$416$	−6.00000	−0.294174
$417$	12.0000	0.587643
$418$	12.0000	0.586939
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	−1.00000	−0.0487950
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	12.0000	0.584151
$423$	2.00000	0.0972433
$424$	2.00000	0.0971286
$425$	−4.00000	−0.194029
$426$	6.00000	0.290701
$427$	14.0000	0.677507
$428$	−4.00000	−0.193347
$429$	12.0000	0.579365
$430$	6.00000	0.289346
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	1.00000	0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	6.00000	0.288009
$435$	0	0
$436$	18.0000	0.862044
$437$	−6.00000	−0.287019
$438$	−14.0000	−0.668946
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	−2.00000	−0.0953463
$441$	1.00000	0.0476190
$442$	24.0000	1.14156
$443$	−20.0000	−0.950229	−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000	−0.950229	−0.475114	+	0.879924i	$0.657593\pi$
$444$	6.00000	0.284747
$445$	10.0000	0.474045
$446$	4.00000	0.189405
$447$	−2.00000	−0.0945968
$448$	−1.00000	−0.0472456
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	1.00000	0.0471405
$451$	12.0000	0.565058
$452$	6.00000	0.282216
$453$	0	0
$454$	14.0000	0.657053
$455$	6.00000	0.281284
$456$	−6.00000	−0.280976
$457$	12.0000	0.561336	0.280668	−	0.959805i	$-0.409444\pi$
$457$	12.0000	0.561336	0.280668	+	0.959805i	$0.409444\pi$
$458$	−6.00000	−0.280362
$459$	−4.00000	−0.186704
$460$	1.00000	0.0466252
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	2.00000	0.0930484
$463$	22.0000	1.02243	0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000	1.02243	0.511213	+	0.859454i	$0.329196\pi$
$464$	0	0
$465$	−6.00000	−0.278243
$466$	−10.0000	−0.463241
$467$	10.0000	0.462745	0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000	0.462745	0.231372	+	0.972865i	$0.425678\pi$
$468$	−6.00000	−0.277350
$469$	2.00000	0.0923514
$470$	2.00000	0.0922531
$471$	−2.00000	−0.0921551
$472$	−12.0000	−0.552345
$473$	−12.0000	−0.551761
$474$	−16.0000	−0.734904
$475$	−6.00000	−0.275299
$476$	4.00000	0.183340
$477$	2.00000	0.0915737
$478$	−18.0000	−0.823301
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	1.00000	0.0456435
$481$	−36.0000	−1.64146
$482$	−20.0000	−0.910975
$483$	−1.00000	−0.0455016
$484$	−7.00000	−0.318182
$485$	2.00000	0.0908153
$486$	1.00000	0.0453609
$487$	−26.0000	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$488$	−14.0000	−0.633750
$489$	−8.00000	−0.361773
$490$	1.00000	0.0451754
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	−6.00000	−0.270501
$493$	0	0
$494$	36.0000	1.61972
$495$	−2.00000	−0.0898933
$496$	−6.00000	−0.269408
$497$	−6.00000	−0.269137
$498$	−2.00000	−0.0896221
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	1.00000	0.0447214
$501$	−14.0000	−0.625474
$502$	−8.00000	−0.357057
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	−1.00000	−0.0445435
$505$	10.0000	0.444994
$506$	−2.00000	−0.0889108
$507$	23.0000	1.02147
$508$	−2.00000	−0.0887357
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	−4.00000	−0.177123
$511$	14.0000	0.619324
$512$	1.00000	0.0441942
$513$	−6.00000	−0.264906
$514$	−14.0000	−0.617514
$515$	8.00000	0.352522
$516$	6.00000	0.264135
$517$	−4.00000	−0.175920
$518$	−6.00000	−0.263625
$519$	0	0
$520$	−6.00000	−0.263117
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	0	0
$523$	24.0000	1.04945	0.524723	−	0.851273i	$-0.324169\pi$
$523$	24.0000	1.04945	0.524723	+	0.851273i	$0.324169\pi$
$524$	12.0000	0.524222
$525$	−1.00000	−0.0436436
$526$	−24.0000	−1.04645
$527$	24.0000	1.04546
$528$	−2.00000	−0.0870388
$529$	1.00000	0.0434783
$530$	2.00000	0.0868744
$531$	−12.0000	−0.520756
$532$	6.00000	0.260133
$533$	36.0000	1.55933
$534$	10.0000	0.432742
$535$	−4.00000	−0.172935
$536$	−2.00000	−0.0863868
$537$	4.00000	0.172613
$538$	30.0000	1.29339
$539$	−2.00000	−0.0861461
$540$	1.00000	0.0430331
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	2.00000	0.0859074
$543$	10.0000	0.429141
$544$	−4.00000	−0.171499
$545$	18.0000	0.771035
$546$	6.00000	0.256776
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	−6.00000	−0.256307
$549$	−14.0000	−0.597505
$550$	−2.00000	−0.0852803
$551$	0	0
$552$	1.00000	0.0425628
$553$	16.0000	0.680389
$554$	−16.0000	−0.679775
$555$	6.00000	0.254686
$556$	12.0000	0.508913
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−6.00000	−0.254000
$559$	−36.0000	−1.52264
$560$	−1.00000	−0.0422577
$561$	8.00000	0.337760
$562$	8.00000	0.337460
$563$	−18.0000	−0.758610	−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000	−0.758610	−0.379305	+	0.925272i	$0.623837\pi$
$564$	2.00000	0.0842152
$565$	6.00000	0.252422
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	6.00000	0.251754
$569$	−4.00000	−0.167689	−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000	−0.167689	−0.0838444	+	0.996479i	$0.526720\pi$
$570$	−6.00000	−0.251312
$571$	16.0000	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$572$	12.0000	0.501745
$573$	12.0000	0.501307
$574$	6.00000	0.250435
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	30.0000	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$578$	−1.00000	−0.0415945
$579$	10.0000	0.415586
$580$	0	0
$581$	2.00000	0.0829740
$582$	2.00000	0.0829027
$583$	−4.00000	−0.165663
$584$	−14.0000	−0.579324
$585$	−6.00000	−0.248069
$586$	6.00000	0.247858
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	1.00000	0.0412393
$589$	36.0000	1.48335
$590$	−12.0000	−0.494032
$591$	−14.0000	−0.575883
$592$	6.00000	0.246598
$593$	26.0000	1.06769	0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000	1.06769	0.533846	+	0.845582i	$0.320746\pi$
$594$	−2.00000	−0.0820610
$595$	4.00000	0.163984
$596$	−2.00000	−0.0819232
$597$	4.00000	0.163709
$598$	−6.00000	−0.245358
$599$	38.0000	1.55264	0.776319	−	0.630340i	$-0.217085\pi$
$599$	38.0000	1.55264	0.776319	+	0.630340i	$0.217085\pi$
$600$	1.00000	0.0408248
$601$	38.0000	1.55005	0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000	1.55005	0.775026	+	0.631929i	$0.217737\pi$
$602$	−6.00000	−0.244542
$603$	−2.00000	−0.0814463
$604$	0	0
$605$	−7.00000	−0.284590
$606$	10.0000	0.406222
$607$	−24.0000	−0.974130	−0.487065	−	0.873366i	$-0.661933\pi$
$607$	−24.0000	−0.974130	−0.487065	+	0.873366i	$0.661933\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	−14.0000	−0.566843
$611$	−12.0000	−0.485468
$612$	−4.00000	−0.161690
$613$	10.0000	0.403896	0.201948	−	0.979396i	$-0.435273\pi$
$613$	10.0000	0.403896	0.201948	+	0.979396i	$0.435273\pi$
$614$	−12.0000	−0.484281
$615$	−6.00000	−0.241943
$616$	2.00000	0.0805823
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	8.00000	0.321807
$619$	−34.0000	−1.36658	−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000	−1.36658	−0.683288	+	0.730149i	$0.739451\pi$
$620$	−6.00000	−0.240966
$621$	1.00000	0.0401286
$622$	−16.0000	−0.641542
$623$	−10.0000	−0.400642
$624$	−6.00000	−0.240192
$625$	1.00000	0.0400000
$626$	10.0000	0.399680
$627$	12.0000	0.479234
$628$	−2.00000	−0.0798087
$629$	−24.0000	−0.956943
$630$	−1.00000	−0.0398410
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	−16.0000	−0.636446
$633$	12.0000	0.476957
$634$	−10.0000	−0.397151
$635$	−2.00000	−0.0793676
$636$	2.00000	0.0793052
$637$	−6.00000	−0.237729
$638$	0	0
$639$	6.00000	0.237356
$640$	1.00000	0.0395285
$641$	48.0000	1.89589	0.947943	−	0.318440i	$-0.103159\pi$
$641$	48.0000	1.89589	0.947943	+	0.318440i	$0.103159\pi$
$642$	−4.00000	−0.157867
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	−1.00000	−0.0394055
$645$	6.00000	0.236250
$646$	24.0000	0.944267
$647$	6.00000	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$648$	1.00000	0.0392837
$649$	24.0000	0.942082
$650$	−6.00000	−0.235339
$651$	6.00000	0.235159
$652$	−8.00000	−0.313304
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	18.0000	0.703856
$655$	12.0000	0.468879
$656$	−6.00000	−0.234261
$657$	−14.0000	−0.546192
$658$	−2.00000	−0.0779681
$659$	18.0000	0.701180	0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000	0.701180	0.350590	+	0.936529i	$0.385981\pi$
$660$	−2.00000	−0.0778499
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	−28.0000	−1.08825
$663$	24.0000	0.932083
$664$	−2.00000	−0.0776151
$665$	6.00000	0.232670
$666$	6.00000	0.232495
$667$	0	0
$668$	−14.0000	−0.541676
$669$	4.00000	0.154649
$670$	−2.00000	−0.0772667
$671$	28.0000	1.08093
$672$	−1.00000	−0.0385758
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	36.0000	1.38667
$675$	1.00000	0.0384900
$676$	23.0000	0.884615
$677$	−2.00000	−0.0768662	−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000	−0.0768662	−0.0384331	+	0.999261i	$0.512237\pi$
$678$	6.00000	0.230429
$679$	−2.00000	−0.0767530
$680$	−4.00000	−0.153393
$681$	14.0000	0.536481
$682$	12.0000	0.459504
$683$	−28.0000	−1.07139	−0.535695	−	0.844411i	$-0.679950\pi$
$683$	−28.0000	−1.07139	−0.535695	+	0.844411i	$0.679950\pi$
$684$	−6.00000	−0.229416
$685$	−6.00000	−0.229248
$686$	−1.00000	−0.0381802
$687$	−6.00000	−0.228914
$688$	6.00000	0.228748
$689$	−12.0000	−0.457164
$690$	1.00000	0.0380693
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	0	0
$693$	2.00000	0.0759737
$694$	−28.0000	−1.06287
$695$	12.0000	0.455186
$696$	0	0
$697$	24.0000	0.909065
$698$	−8.00000	−0.302804
$699$	−10.0000	−0.378235
$700$	−1.00000	−0.0377964
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	−6.00000	−0.226455
$703$	−36.0000	−1.35777
$704$	−2.00000	−0.0753778
$705$	2.00000	0.0753244
$706$	−26.0000	−0.978523
$707$	−10.0000	−0.376089
$708$	−12.0000	−0.450988
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	6.00000	0.225176
$711$	−16.0000	−0.600047
$712$	10.0000	0.374766
$713$	−6.00000	−0.224702
$714$	4.00000	0.149696
$715$	12.0000	0.448775
$716$	4.00000	0.149487
$717$	−18.0000	−0.672222
$718$	20.0000	0.746393
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	1.00000	0.0372678
$721$	−8.00000	−0.297936
$722$	17.0000	0.632674
$723$	−20.0000	−0.743808
$724$	10.0000	0.371647
$725$	0	0
$726$	−7.00000	−0.259794
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	6.00000	0.222375
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	−24.0000	−0.887672
$732$	−14.0000	−0.517455
$733$	50.0000	1.84679	0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000	1.84679	0.923396	+	0.383849i	$0.125402\pi$
$734$	−8.00000	−0.295285
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	4.00000	0.147342
$738$	−6.00000	−0.220863
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	6.00000	0.220564
$741$	36.0000	1.32249
$742$	−2.00000	−0.0734223
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	−6.00000	−0.219971
$745$	−2.00000	−0.0732743
$746$	−26.0000	−0.951928
$747$	−2.00000	−0.0731762
$748$	8.00000	0.292509
$749$	4.00000	0.146157
$750$	1.00000	0.0365148
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	2.00000	0.0729325
$753$	−8.00000	−0.291536
$754$	0	0
$755$	0	0
$756$	−1.00000	−0.0363696
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	20.0000	0.726433
$759$	−2.00000	−0.0725954
$760$	−6.00000	−0.217643
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	−2.00000	−0.0724524
$763$	−18.0000	−0.651644
$764$	12.0000	0.434145
$765$	−4.00000	−0.144620
$766$	0	0
$767$	72.0000	2.59977
$768$	1.00000	0.0360844
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	2.00000	0.0720750
$771$	−14.0000	−0.504198
$772$	10.0000	0.359908
$773$	−38.0000	−1.36677	−0.683383	−	0.730061i	$-0.739492\pi$
$773$	−38.0000	−1.36677	−0.683383	+	0.730061i	$0.739492\pi$
$774$	6.00000	0.215666
$775$	−6.00000	−0.215526
$776$	2.00000	0.0717958
$777$	−6.00000	−0.215249
$778$	−6.00000	−0.215110
$779$	36.0000	1.28983
$780$	−6.00000	−0.214834
$781$	−12.0000	−0.429394
$782$	−4.00000	−0.143040
$783$	0	0
$784$	1.00000	0.0357143
$785$	−2.00000	−0.0713831
$786$	12.0000	0.428026
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−14.0000	−0.498729
$789$	−24.0000	−0.854423
$790$	−16.0000	−0.569254
$791$	−6.00000	−0.213335
$792$	−2.00000	−0.0710669
$793$	84.0000	2.98293
$794$	−14.0000	−0.496841
$795$	2.00000	0.0709327
$796$	4.00000	0.141776
$797$	−46.0000	−1.62940	−0.814702	−	0.579880i	$-0.803099\pi$
$797$	−46.0000	−1.62940	−0.814702	+	0.579880i	$0.803099\pi$
$798$	6.00000	0.212398
$799$	−8.00000	−0.283020
$800$	1.00000	0.0353553
$801$	10.0000	0.353333
$802$	20.0000	0.706225
$803$	28.0000	0.988099
$804$	−2.00000	−0.0705346
$805$	−1.00000	−0.0352454
$806$	36.0000	1.26805
$807$	30.0000	1.05605
$808$	10.0000	0.351799
$809$	−22.0000	−0.773479	−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000	−0.773479	−0.386739	+	0.922189i	$0.626399\pi$
$810$	1.00000	0.0351364
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	0	0
$813$	2.00000	0.0701431
$814$	−12.0000	−0.420600
$815$	−8.00000	−0.280228
$816$	−4.00000	−0.140028
$817$	−36.0000	−1.25948
$818$	34.0000	1.18878
$819$	6.00000	0.209657
$820$	−6.00000	−0.209529
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	−6.00000	−0.209274
$823$	46.0000	1.60346	0.801730	−	0.597687i	$-0.203913\pi$
$823$	46.0000	1.60346	0.801730	+	0.597687i	$0.203913\pi$
$824$	8.00000	0.278693
$825$	−2.00000	−0.0696311
$826$	12.0000	0.417533
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	1.00000	0.0347524
$829$	20.0000	0.694629	0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000	0.694629	0.347314	+	0.937749i	$0.387094\pi$
$830$	−2.00000	−0.0694210
$831$	−16.0000	−0.555034
$832$	−6.00000	−0.208013
$833$	−4.00000	−0.138592
$834$	12.0000	0.415526
$835$	−14.0000	−0.484490
$836$	12.0000	0.415029
$837$	−6.00000	−0.207390
$838$	−4.00000	−0.138178
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	−1.00000	−0.0345033
$841$	−29.0000	−1.00000
$842$	6.00000	0.206774
$843$	8.00000	0.275535
$844$	12.0000	0.413057
$845$	23.0000	0.791224
$846$	2.00000	0.0687614
$847$	7.00000	0.240523
$848$	2.00000	0.0686803
$849$	0	0
$850$	−4.00000	−0.137199
$851$	6.00000	0.205677
$852$	6.00000	0.205557
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	14.0000	0.479070
$855$	−6.00000	−0.205196
$856$	−4.00000	−0.136717
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	12.0000	0.409673
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	6.00000	0.204598
$861$	6.00000	0.204479
$862$	−24.0000	−0.817443
$863$	−32.0000	−1.08929	−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000	−1.08929	−0.544646	+	0.838666i	$0.683336\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	2.00000	0.0679628
$867$	−1.00000	−0.0339618
$868$	6.00000	0.203653
$869$	32.0000	1.08553
$870$	0	0
$871$	12.0000	0.406604
$872$	18.0000	0.609557
$873$	2.00000	0.0676897
$874$	−6.00000	−0.202953
$875$	−1.00000	−0.0338062
$876$	−14.0000	−0.473016
$877$	−12.0000	−0.405211	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	−12.0000	−0.405211	−0.202606	+	0.979260i	$0.564941\pi$
$878$	26.0000	0.877457
$879$	6.00000	0.202375
$880$	−2.00000	−0.0674200
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	1.00000	0.0336718
$883$	−24.0000	−0.807664	−0.403832	−	0.914833i	$-0.632322\pi$
$883$	−24.0000	−0.807664	−0.403832	+	0.914833i	$0.632322\pi$
$884$	24.0000	0.807207
$885$	−12.0000	−0.403376
$886$	−20.0000	−0.671913
$887$	30.0000	1.00730	0.503651	−	0.863907i	$-0.331990\pi$
$887$	30.0000	1.00730	0.503651	+	0.863907i	$0.331990\pi$
$888$	6.00000	0.201347
$889$	2.00000	0.0670778
$890$	10.0000	0.335201
$891$	−2.00000	−0.0670025
$892$	4.00000	0.133930
$893$	−12.0000	−0.401565
$894$	−2.00000	−0.0668900
$895$	4.00000	0.133705
$896$	−1.00000	−0.0334077
$897$	−6.00000	−0.200334
$898$	−18.0000	−0.600668
$899$	0	0
$900$	1.00000	0.0333333
$901$	−8.00000	−0.266519
$902$	12.0000	0.399556
$903$	−6.00000	−0.199667
$904$	6.00000	0.199557
$905$	10.0000	0.332411
$906$	0	0
$907$	10.0000	0.332045	0.166022	−	0.986122i	$-0.446908\pi$
$907$	10.0000	0.332045	0.166022	+	0.986122i	$0.446908\pi$
$908$	14.0000	0.464606
$909$	10.0000	0.331679
$910$	6.00000	0.198898
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	−6.00000	−0.198680
$913$	4.00000	0.132381
$914$	12.0000	0.396925
$915$	−14.0000	−0.462826
$916$	−6.00000	−0.198246
$917$	−12.0000	−0.396275
$918$	−4.00000	−0.132020
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	1.00000	0.0329690
$921$	−12.0000	−0.395413
$922$	2.00000	0.0658665
$923$	−36.0000	−1.18495
$924$	2.00000	0.0657952
$925$	6.00000	0.197279
$926$	22.0000	0.722965
$927$	8.00000	0.262754
$928$	0	0
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	−6.00000	−0.196748
$931$	−6.00000	−0.196642
$932$	−10.0000	−0.327561
$933$	−16.0000	−0.523816
$934$	10.0000	0.327210
$935$	8.00000	0.261628
$936$	−6.00000	−0.196116
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	2.00000	0.0653023
$939$	10.0000	0.326338
$940$	2.00000	0.0652328
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−2.00000	−0.0651635
$943$	−6.00000	−0.195387
$944$	−12.0000	−0.390567
$945$	−1.00000	−0.0325300
$946$	−12.0000	−0.390154
$947$	−4.00000	−0.129983	−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000	−0.129983	−0.0649913	+	0.997886i	$0.520702\pi$
$948$	−16.0000	−0.519656
$949$	84.0000	2.72676
$950$	−6.00000	−0.194666
$951$	−10.0000	−0.324272
$952$	4.00000	0.129641
$953$	22.0000	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$954$	2.00000	0.0647524
$955$	12.0000	0.388311
$956$	−18.0000	−0.582162
$957$	0	0
$958$	−24.0000	−0.775405
$959$	6.00000	0.193750
$960$	1.00000	0.0322749
$961$	5.00000	0.161290
$962$	−36.0000	−1.16069
$963$	−4.00000	−0.128898
$964$	−20.0000	−0.644157
$965$	10.0000	0.321911
$966$	−1.00000	−0.0321745
$967$	−26.0000	−0.836104	−0.418052	−	0.908423i	$-0.637287\pi$
$967$	−26.0000	−0.836104	−0.418052	+	0.908423i	$0.637287\pi$
$968$	−7.00000	−0.224989
$969$	24.0000	0.770991
$970$	2.00000	0.0642161
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	1.00000	0.0320750
$973$	−12.0000	−0.384702
$974$	−26.0000	−0.833094
$975$	−6.00000	−0.192154
$976$	−14.0000	−0.448129
$977$	46.0000	1.47167	0.735835	−	0.677161i	$-0.236790\pi$
$977$	46.0000	1.47167	0.735835	+	0.677161i	$0.236790\pi$
$978$	−8.00000	−0.255812
$979$	−20.0000	−0.639203
$980$	1.00000	0.0319438
$981$	18.0000	0.574696
$982$	−36.0000	−1.14881
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−6.00000	−0.191273
$985$	−14.0000	−0.446077
$986$	0	0
$987$	−2.00000	−0.0636607
$988$	36.0000	1.14531
$989$	6.00000	0.190789
$990$	−2.00000	−0.0635642
$991$	−48.0000	−1.52477	−0.762385	−	0.647124i	$-0.775972\pi$
$991$	−48.0000	−1.52477	−0.762385	+	0.647124i	$0.775972\pi$
$992$	−6.00000	−0.190500
$993$	−28.0000	−0.888553
$994$	−6.00000	−0.190308
$995$	4.00000	0.126809
$996$	−2.00000	−0.0633724
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	−20.0000	−0.633089
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.bg.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.bg.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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